Yeah, I ended up removing it. Though I felt the design was very clever (and I really loved the reload mechanic) the majority of feedback I received commented that just trying to keep the Iron Egg from leaving the screen itself was an engaging challenge. On top of the fact that I had run out of token count and that I wanted to implement a few other things (i.e. the Iron Egg bouncing off the ship on contact), the shot limit had to get cut.
That said: I am considering uploading a version of the game prior to the shot limit removal ("Vanilla" Scramble, Scramble!!) and leaving a comment in the developer's notes that the shot limit is the "intended experience."
EDIT: Also just want to add one tidbit!
Take what I say right here with a massive grain of salt because I'm a very inexperienced, hobbyist gamedev:
One big lesson I've learned from this project is that even if I think an idea is very good (i.e. limiting bullets in order to artificially enforce player engagement with the Iron Egg's positioning) it doesn't necessarily mean the player will enjoy it. The most common feedback I'd get after explaining why the shot limit was implemented was:
"But it's not fun :C why you gotta narc my fun?"
If I received that comment only once I'd still feel confident in my gut feeling that the game mechanic was fine. But after receiving that comment from many people, I realized it just had to go.
Lesson learned! Just because a mechanic is theoretically defensible does not mean most of your players will like it.